Documentation/Calc Functions/Z.TEST

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Function name:

Z.TEST

Category:

Statistical Analysis

Summary:

Calculates the one-tailed cumulative probability value of a Z-test. This is the probability of observing a sample mean as large or larger than the mean of the given sample for samples drawn from a normal distribution.

Syntax:

Z.TEST(Data; mu[;Sigma])

Returns:

Returns a real number which is the one-tailed cumulative probability value of a Z-test for data sample Data, mean value mu and standard deviation as Sigma. It ranges from 0 to 1, i.e. [0,1].

Arguments:

Data is an array or a reference to a range of cells which is the given sample, drawn from a normally distributed population.

mu is a real number or a reference to the cell containing that number which is the known mean of the population.

Sigma is a positive real number or a reference to the cell containing that number which is the known standard deviation of the population. If omitted, the standard deviation of the given sample is used.

  • If Sigma is negative or zero then the function returns an error value.
  • If mu or Sigma is not a real number then the function returns a #VALUE! error.

Additional details:

  • It is such that Z.TEST(Data,mu) = 1 - NORM.S.DIST((Average(Data)-mu)/(sigma/√n), TRUE()) or for the case where sigma is omitted and s is the standard deviation of the Data, Z.TEST(Data,mu) = 1 - NORM.S.DIST((Average(Data)-mu)/(s/√n), TRUE())
  • With sample being the mean of Data and
Ztest.png

The formula for Z.TEST is:

Ztestf.png

Examples:

Formula Description Returns
=Z.TEST(A1:A7;8) where A1:A7 contains 5,5.9,4.1,7.3,2.8,1.2,6 The function calculates the one-tailed cumulative probability value of a Z-test for data sample. Here Sigma is not mentioned hence standard deviation of the data is used. 0.999991103497123
=Z.TEST(A1:A7;8;10) where A1:A7 contains 5,5.9,4.1,7.3,2.8,1.2,6 The function calculates the one-tailed cumulative probability value of a Z-test for data sample. 0.814813741690979
=Z.TEST({5;-5.9;4.1;-7.3;2.8;1.2;0};8;10) The function calculates the one-tailed cumulative probability value of a Z-test for data sample. 0.983013023242316
=Z.TEST(A1:A7;8;0) where A1:A7 contains 5,5.9,4.1,7.3,2.8,1.2,6 The function returns an error value for Sigma less than equal to zero. Err:502

Related LibreOffice functions:

ZTEST

TTEST

FTEST

T.TEST

F.TEST

NORM.DIST

NORM.S.DIST

AVERAGE

ODF standard:

None

Equivalent Excel functions:

Z.TEST